If Zhonya's is hidden and I have two units on the board that are going to die by a battle, do I choose whose saving with my Zhonya's?

Yes, you choose which unit to save.

According to the RiftJudge FAQ regarding Zhonya's Hourglass (FAQ 6895, 1988, and 1042): when multiple units die simultaneously from combat damage, the controller of the Zhonya's Hourglass replacement effect chooses which unit's death is replaced.

Here is the breakdown of how this works:

1. Timing: Because this is combat damage, all units at that battlefield die simultaneously. You must flip and activate your hidden Zhonya's Hourglass as a reaction before the damage is assigned during the showdown (Rule 373). You cannot wait to see the results of the damage; you must act while you still have priority.
2. Replacement: Since you are replacing a death event with your Zhonya's Hourglass, and you have two units dying at the same time, you (as the controller of the replacement effect) choose which one of those deaths to apply the replacement to (Rule 373).
3. Result: The chosen unit is saved (healed, exhausted, and recalled to your base), and the other unit will proceed to die as normal.

This interpretation is supported by multiple FAQs confirming that for simultaneous deaths, the controller of the replacement effect chooses the order of application.